We consider utility maximization problem for semi- martingale models depending on a random factor . We reduce initial maximization problem to the conditional one, given = u, which we solve using dual approach. For HARA utilities we con- sider information quantities like Kullback-Leibler information and Hellinger integrals, and corresponding information processes. As a particular case we study exponential Levy models depending on random factor. In that case the information processes are deter- ministic and this fact simplify very much indi erence price calcu- lus. Then we give the equations for indi erence prices. We show that indi erence price for seller and minus indi erence price for buyer are risk measures. Finally, we apply the results to Geo- metric Brownian motion case. Using identity in law technique we give the explicit expression for information quantities. Then, the previous formulas for indi erence price can be applied.
UTILITY MAXIMISATION AND UTILITY INDIFFERENCE PRICE FOR EXPONENTIAL SEMI-MARTINGALE MODELS WITH RANDOM FACTOR